Introduction – What is calculus?
Chapter 2 – Limits and derivatives
2.1 The tangent and velocity problems
2.2 The limit of a function
2.3 Calculating limits using the limit laws
2.4 The precise definition of a limit
2.5 Continuity
2.6 Limits at infinity; horizontal asymptotes
2.7 Derivatives and rates of change
2.8 The derivative as a function
Chapter 3 – Differentiation Rules
3.1 Derivatives of polynomials and exponential functions;
see also 1.5
3.2 The Product and Quotient Rules
3.3 Derivatives of trigonometric functions
3.4 The Chain Rule
3.5 Implicit differentiation
3.6 Derivatives of logarithmic functions; see also 1.6
3.7 Rates of change in the natural and social sciences
3.8 Exponential growth and decay
3.9 Related rates
3.10 Linear approximations and differentials
Chapter 4 – Applications of Differentiation
4.1 Maximum and minimum values
4.2 The Mean Value Theorem
4.3 How derivatives affect the shape of a graph
4.4 Indeterminate forms and L’Hospital’s Rule
4.7 Optimization problems
4.8 Newton’s Method
4.9 Antiderivatives
Chapter 5 – Integrals (introduction)
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